We study an "above guarantee" version of the {\sc Longest Path} problem in directed graphs: We are given a graph $G$, two vertices $s$ and $t$ of $G$, and a non-negative integer $k$, and the objective is to determine whether $G$ contains a path of length at least $dist_G(s,t) +k$ where $dist_G(s,t)$ is the length of a shortest path from $s$ to $t$ in $G$ (assuming that one exists). We show that the problem is fixed parameter tractable (FPT) parameterized by $k$ in the class of graphs where {\sc $2$-Disjoint Paths} problem is polynomial time solvable.
翻译：我们在定向图表中研究“超长路径”问题的“高于保证”版本:我们得到一张图表$,两面顶点$和美元美元,还有非负整数美元,目标是确定$是否包含至少以美元计价的长度路径+k$,其中美元是美元至美元以美元计价的最短路径的长度(假设存在一条)。 我们显示,在每张图表中,问题是以美元计价、美元计价、美元计价、美元计价、美元计价、美元计价、美元计价、美元计价、美元计价、美元计价、美元计价、美元计价、美元计价、美元计价、美元计价、美元计价、美元计价、美元计价、美元计价。
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